5 Answers
5

Most states choose Presidential electors based on the candidate who got the most votes in the November election, but not all do. In particular, Nebraska (which has 3 congressional districts and therefore 5 electoral votes) allocates 2 electors to the state-wide winner, and each of the other 3 to the winner in each congressional district. In the 2008 election, Nebraska cast 4 votes for McCain and 1 for Obama, who won a majority of the vote in one district.

Maine has a similar rule, but I don't believe it's split its votes since it established that rule.

But electors are not Constitutionally required to vote as they committed (though there may be penalties under state law). The Constitution leaves it to each state legislature to decide how electors are chosen. All states currently do so by popular vote, but that hasn't always been the case.

There have been a few cases of "faithless electors". Most recently, a 2000 Washington, D.C. elector refused to cast a vote to protest D.C.'s lack of representation in Congress, and a 2004 Minnesota elector wrote the wrong name on the ballot, apparently accidentally.

States Electors aren't really bound to the popular vote, there have been cases where the popular vote did not decide the winner-take-all voting system we have; I note this because Main and Nebraska do have a different system as Keith notes. That system divides up the votes, and while this typically matches the Popular vote it has not always been so.

I'm not clear if you are asking about specific states, or in general for the elections where the national popular vote did not match the Electoral College - which gave the election to someone else. There are not really that many cases of this:

1800 election of Aaron Burr and Thomas Jefferson ended up as a tie with 73 electoral votes each, which put the decision to the House of Representatives and the result of this was the 12th Amendment

1824 had a four way contest with Andrew Jackson, John Quincy Adams, William Crawford, and Henry Clay all gaining votes but not a majority, which put the decision of the election to the House of Representatives (according to the 12th Amendment). In this case John Quincy Adams received the majority of the House votes, even with Jackson getting the most electoral votes, in this case the election went where neither the popular count or electoral count showed a victor

1888 election of Benjamin Harrison was a case where Harrison had some small majorities in some of the bigger states, which gave him a larger Electoral College count which gave him the election

2000 election of George W Bush and Al Gore often notes that Al Gore won the majority of the popular vote, but the decision by the Supreme Court gave the election to Bush. There is plenty of evidence on who won the votes on either side, though I tend to side with the evidence that it was Gore, this was the year of the Butterfly Ballot and hanging chad's

Remember though, that early elections were often handled by Congress who promoted candidates, voting was at first limited to only landed males and extended later so comparing the votes between early elections and present day needs to take this all into account.

The general idea behind the Electoral College is that the states pick Electors, they get 1 each for each congressmen and senator they have (iow: at least 3 for every state, more for bigger ones), and the Electoral College decides, based on majoriy vote, who is President.

Nits:

It is up to the states how they pick their Electors. It would be perfectly OK for the Governor or the state legislature's ruling party to just assign them, if the people of that state would put up with such a system. It's been done in the past. Right now all states allow their citizens to directly vote for electors, and in all but two states the majority candidate gets all the electors. However, that's for the states to decide. Originally, almost no states directly elected their EC representatives, so it would be fair to say that in most early elections, the EC voted for candidates that had not been voted on by "the people".

Electors are free to vote how they please. Half of the states try to legally require their electors to vote for who they promised to vote for, but Federal law has no such requirement.

They might not get to decide. If there's no majority winner, the election goes to the newly-elected House of Representatives (but on a one-vote-per-state basis). This has not happened in nearly 200 years, and really could only happen in today's universe in the case of a 270-270 tie. (There's an even more breathtakingly unlikely scenario where the Senate could end up indirectly picking the President, but let's not get into that)

Typically, it's the candidate who got a plurality of the popular vote, not necessarily the majority. Third-party candidates can easily result in no candidate getting an absolute majority (more than 50%). As for your third point, if a third-party candidate got some electoral votes, that could send the election to the House. That's not particularly likely.
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Keith ThompsonOct 23 '12 at 20:44

@KeithThompson - I belive the term I used was not "in today's universe". I stand by that. No third party has gotten a significant number of electoral votes since 1968. If the "universe" changes, I promise to come back and edit my wording. :-)
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T.E.D.♦Oct 23 '12 at 21:16

If Ross Perot had actually run within a party he could have changed that
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MichaelFOct 24 '12 at 9:47

@MichaelF - No, he couldn't have. This might make a good question, but in 260 words or less, the only way to get the kind of 3-way splits we last saw in 1968 is for one of the parties to have a purely regional powerbase. Otherwise, Duveger's Law applies. Perot's campaign had entirely national themes, so there was no way for him to win a state without displacing the weaker of the other two parties nationally (iow: become one of the two big parties himself). For example, 1968 only happened because conservative southerners just couldn't bring themselves to vote Republican.
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T.E.D.♦Oct 24 '12 at 17:58

@T.E.D. I disagree, if he had been able to build up his support he could have actually made enough progress to pull in electoral votes in some states and he did try with whatever party he built at the time but there was not enough disaffection with the other two parties to carry this. The Tea Party shows it could be done if outside of the framework of either the R or D. I'll let it go at that.
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MichaelFOct 24 '12 at 20:23

There has never been a case where the Electoral College AS A WHOLE, went against the electoral votes generated by popular vote.

That said, there have been cases where individual ELECTORS went against their state's vote. One example I can think of is in 1988, when the popular vote of the state of West Virginia wen for Dukakis. One lady elector from that state cast her vote for Lloyd Bentsen (Dukakis' running mate), for President and Dukakis for Vice-President. So Dukakis actually got only 110 electoral votes instead of the 111 he was entitled to.